Answer
$P(king)=\frac{1}{13}\approx0.077$
$P(king~|~heart)=\frac{1}{13}\approx0.077$
The events "the card drawn is a king" and "the card is a heart" are independent.
Work Step by Step
The sample space: all the 52 cards from a standard 52-card deck. So, N(S) = 52.
There are 4 king cards. So N(king) = 4.
We can compute the probability that the card drawn is a king using the Classical Method (see page 259):
$P(king)=\frac{N(king)}{N(S)}=\frac{4}{52}=\frac{1}{13}\approx0.077.$
There are 13 heart cards. So, N(heart) = 13.
There is only one king among the heart cards. So, N(king and heart) = 1.
Now, using the Conditional Probability Rule (see page 288):
$P(king~|~heart)=\frac{N(king~and~heart)}{N(heart)}=\frac{1}{13}\approx0.077.$
$P(king~|~heart)=P(king)$. It means that the events "the card drawn is a king" and "the card is a heart" are independent.
